The Night King was the first of the White Walkers. He was one of the First Men before he was turned into something else by the Children of the Forest.
According to Old Nan, the Night's King may in fact be (hold on to your small clothes) a Stark! If that isn't enough, legend has it that the Night's King was not just any Stark, he was King Brandon Stark's brother—or possibly Brandon Stark himself!
She said some people believe Night's King was a Bolton, a Magnar of Skagos, an Umber, a Flint, a Norrey, or a Woodfoot. However, she identifies Night's King as a Stark of Winterfell and brother to the King of Winter and suggests his name was Brandon.
Aside from being a symbol of death, the creation of the Night King was a way to add more history to the fictional universe. The series had the opportunity to dive deeper into the mythology of White Walkers by tying in their creation to the Children of the Forest and the First Men.
All of that changed when Bran entered the picture as the Three-Eyed Raven. This introduction gave the Night King a true motive outside the typical megalomania of Big Bads. By wiping out the Three-Eyed Raven, he would be wiping out all memories of the previous world and fully ushering in his new era.
No, the Night King is not a Targaryen.
In the books, however, the story of the Night King is slightly different. The Night King isn't the leader of the White Walkers. Instead, he's a legendary historical figure who supposedly betrayed the Night's Watch to marry a “corpse queen” and then crowned himself a king.
The final key argument against Bran being Game of Thrones' big bad is a pretty simple one. The Night King is a show-only character, he doesn't exist in the books (at least not yet). Bran being the Night King would be a gigantic step away from the source material.
In Season 8, Bran reveals that the Night King wants to destroy him because he holds all of the history of man.
TL;DR version: The Night's King is interested in Jon Snow because he sees some of himself in the current Lord Commander. “The gathering gloom put Bran in mind of another of Old Nan's stories, the tale of Night's King.
They're [the Night King's ice power and Dany's fire] two polar opposites, so they can't really be killed by each other.” This posit calls to mind Harry Potter and Voldemort's battles in the film series where their powers basically cancel each other out.
The Night King uses his power to raise Viserion from the dead, the same way he's raised wights from the dead. That means Viserion is filled with the Night King's magic, which is why his fire is blue and why the Night King is able to use him as a mount.
No, Hodor is not a Targaryen.
In the TV series, it's revealed that Hodor was originally a stable hand called Wylis who was essentially lobotomized when Bran attempted to warg into Wylis, connecting him with present-day Hodor who was holding back an army of wights.
The Night King Turns Craster's Sons Into White Walkers
As for why babies, and not adults, are candidates for transformation into White Walkers, this is likely because infants are easier to mold into whatever the Night King wishes.
During the Battle of Winterfell, twelve White Walkers enter Winterfell along with the Night King to kill Bran Stark. All the White Walkers were destroyed after Arya killed the Night King.
As the Three-Eyed Raven, Bran has the ability of greensight, which means he can see events in the past, present, and future through visions. Killing Bran would essentially erase all memory of mankind. Samwell Tarly explains it pretty well in the scene.
Senseless, Bran dreams of his falling from the tower and of a three-eyed crow that offers to teach him to fly. With the crow's guidance, Bran wakes; but having been crippled by the fall, he is unable to walk.
This is why the Night King was initially able to psychically track Bran before he grabbed him by the arm and marked him in “The Door,” instantly sensing and seeing him (and the previous Three Eyed Ravens) when Bran warged into an animal nearby.
The Night King doesn't really care about Bran Stark, but he cares very much about The Three-Eyed Raven, which is the magical being Bran Stark has become. According to Bran, who is all-knowing at this point, the Night King's real goal isn't just to rule Westeros, but to erase it.
The Night King was created by TCOTF as an agent of death. So The Night King is the only being who didn't come out of his journey through The Wiernet as A 3 Eyed Raven. He came out as a perversion of The 3 Eyed Raven.
According to this Reddit user, the Children of the Forest created the Three-Eyed Raven to defeat the Night King. Now, Bran – aka the Three-Eyed Raven — is the only one who can stop the Night King.
As the two dragons struggled in the Battle Above the Gods Eye, Daemon plunged from Caraxes, wielding his sword Dark Sister and stabbing it into Aemond's remaining eye. Both dragons crashed into the Gods Eye, and Vhagar drowned with Aemond's body still chained to the saddle while Caraxes died on the shore.
2 Daemon Is A Distant Great-Uncle Of Daenerys But Also Her Sixth Great-Grandfather.
The children of Rhaenyra and Daemon Targaryen
(Yes, they're uncle and niece. Targaryens are big into incest, just go with it.) And here's where the SPOILERS start.